Abstract
The origin of the Cole-Cole dielectric spectral equation is investigated by considering its attendant susceptibility as originating in the Laplace transform of the fractional Fokker-Planck equation. The eigenvalues of the solution point to the interaction of the dipole with its local molecular conditions, as dictated by the local fields involved, as the origin of the spectral broadening (described by the parameter α). This view is compared to ideas in the literature pointing to a dipole-matrix interaction as the cause of spectral broadening. The question is posed concerning what information exists in the as yet unexplored element of the CC function, namely the dielectric strength, Δε. In this context a new derivation of Fröhlich’s B(T) function is proposed, that relies on fully accessible experimental values only and is capable of unifying all parameters of the Cole-Cole function via the calculated correlation between dipoles. This function is demonstrated via an electron hopping process, exhibiting Cole-Cole dielectric behavior, observed in a ferroelectric KTN crystal.
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Acknowledgments
The authors would like to thank Prof. Aharon J. Agranat for providing the crystal analyzed in the study and for helpful discussions. The authors would also like to thank Prof. Marian Paluch for providing the pressure measurements which proved to be a vital ingredient for confirming the theory.
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Ishai, P.B., Lerner, S., Puzenko, A.A., Feldman, Y. (2013). Anomalous Diffusion, Cole-Cole Relaxation and the Space in Which They Occur: Puzzles and Problems. In: Kalmykov, Y. (eds) Recent Advances in Broadband Dielectric Spectroscopy. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5012-8_3
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